The investigation of the vibrational disturbances of the Hubble Space Telescope that were discovered soon after deployment in orbit is described in detail. It was found that the disturbances were particularly evident during orbital day-night crossings, and that the magnitude of the disturbances was considerably larger than the design jitter requirement. This paper describes the process by which the vibrations were characterized and isolated to a particular mechanism. The analysis of the flight data and comparisons with computer simulation results showed that the source of the disturbances was the thermally driven deformation of the solar arrays in conjunction with frictional effects in the array mechanisms. The control system was successfully modified to attenuate the disturbances to tolerable levels pending mechanical and thermal redesign of the solar arrays. The new arrays were installed during the first Space Telescope servicing mission, and in combination with the enhanced control system algorithm reduced the disturbances to satisfactory levels.